arXiv Machine Learning By Minh Vu, Andrey Y. Lokhov, Marc Vuffray

Symmetric Linear Dynamical Systems are Learnable from Few Observations

Read the original on arXiv Machine Learning →

arXiv:2512. 05337v2 Announce Type: replace-cross Abstract: We consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv Machine Learning
Sep 10

Low-Rank Plus Sparse Matrix Transfer Learning under Growing Representations and Ambient Dimensions

The paper introduces a transfer learning framework for structured matrix estimation when both the ambient dimension and the intrinsic representation grow over time. It models the target parameter as an embedded source component plus low‑rank innovations and sparse edits, and proposes an anchored alternating projection estimator that preserves the transferred subspace while estimating only the new components. Deterministic error bounds are derived that separate target noise, representation growth, and source estimation error, showing improved rates when rank and sparsity increments are small, and the framework is applied to Markov transition matrix estimation and structured covariance estimation with theoretical guarantees and empirical validation.

By Jinhang Chai, Xuyuan Liu, Elynn Chen, Yujun Yan
arXiv Machine Learning
Sep 18

Demystifying Linear Operator Learning for Control Systems

The paper introduces a structured method for learning linear operators in control systems using data. It leverages the framework of (semi)groups for evolution equations to establish structural assumptions and applies inverse‑problems theory to analyze learning algorithms, revealing error decompositions, convergence guarantees, and optimal regularization. Focusing on bounded operators on Hilbert spaces, the authors derive a convergent estimator for time‑varying systems, illustrating the practical power of their approach.

By Max Beier, Nicolas Hoischen, Sandra Hirche, Petar Bevanda